An Introduction to MATLAB II

Transcription

1 Lab of COMP 319 An Introduction to MATLAB II Lab tutor : Gene Yu Zhao Mailbox: csyuzhao@comp.polyu.edu.hk or genexinvivian@gmail.com Lab 2: 16th Sep,

2 Outline of Lab 2 Review of Lab 1 Matrix in Matlab MATLAB Graphics More Practices 2

3 Outline of Lab 2 Review of Lab 1 Matrix in Matlab MATLAB Graphics More Practices 3

4 Review of Lab 1 Compute the following quantities sin 2 ( π / 4) + cos 2 ( π / 4) iπ e +1 ( 1+ 3i) /(1 3i) x = 32π ; y = cos x 2 sin 2 x 4

5 Answers 5

6 Outline of Lab 2 Review of Lab 1 Matrix in Matlab MATLAB Graphics More Practices 6

7 MATLAB Matrices MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored. Vectors are special forms of matrices and contain only one row OR one column. Scalars are matrices with only one row AND one column 7

8 MATLAB Matrices A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows:» a_value=23 a_value = 23 8

9 MATLAB Matrices A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):» rowvec = [12, 14, 63] or rowvec = [ ] rowvec =

10 MATLAB Matrices A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons):» colvec = [13 ; 45 ; -2] colvec =

11 MATLAB Matrices A matrix can be created in MATLAB as follows (note the commas AND semicolons):» matrix = [1, 2, 3 ; 4, 5,6 ; 7, 8, 9] matrix =

12 Extracting a Sub-Matrix A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices, the rows and columns. The syntax is: sub_matrix = matrix ( r1 : r2, c1 : c2 ) ; where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix. 12

13 MATLAB Matrices A column vector can be extracted from a matrix. As an example we create a matrix below:» matrix=[1,2,3;4,5,6;7,8,9] matrix = Here we extract column 2 of the matrix and make a column vector:» col_two=matrix( :, 2) col_two =

14 MATLAB Matrices A row vector can be extracted from a matrix. As an example we create a matrix below:» matrix=[1,2,3;4,5,6;7,8,9] matrix = Here we extract row 2 of the matrix and make a row vector. Note that the 2:2 specifies the second row and the 1:3 specifies which columns of the row.» rowvec=matrix(2 : 2, 1 : 3) rowvec =

15 Matrices transpose a vector x = [ ] x = transpose y = x y =

16 Scalar - Matrix Addition»a=3;» b=[1, 2, 3;4, 5, 6] b = » c= b+a % Add a to each element of b c =

17 Scalar - Matrix Subtraction»a=3;» b=[1, 2, 3;4, 5, 6] b = » c = b - a %Subtract a from each element of b c =

18 Scalar - Matrix Multiplication»a=3;» b=[1, 2, 3; 4, 5, 6] b = » c = a * b % Multiply each element of b by a c =

19 Scalar - Matrix Division»a=3;» b=[1, 2, 3; 4, 5, 6] b = » c = b / a % Divide each element of b by a c =

20 Other operators [ ] concatenation ( ) subscription x = [ zeros(1,3) ones(1,2) ] x = x = [ ] x = y = x(2) y = 3 y = x(2:4) y =

21 Outline of Lab 2 Review of Lab 1 Matrix in Matlab MATLAB Graphics More Practices 21

22 Matlab Graphics t_vect=0:0.01:2*pi; X_vect=16*(sin(t_vect) ).^3; Y_vect=13*cos(t_vect)- 5*cos(2*t_vect)- 2*cos(3*t_vect)- cos(4*t_vect fill(x_vect,y_vect,'r' ); 22

23 Matlab Graphics x = 0:pi/100:2*pi; y = sin(x); plot(x,y) xlabel('x = 0:2\pi') ylabel('sine of x') title('plot of the Sine Function') 23

24 Multiple Graphs t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2); plot(t,y1,t,y2) grid on 24

25 Multiple Plots t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2); subplot(2,2,1) plot(t,y1) subplot(2,2,2) plot(t,y2) 25

26 Graph Functions (summary) plot linear plot stem discrete plot grid add grid lines xlabel add X-axis label ylabel add Y-axis label title add graph title subplot divide figure window figure create new figure window pause wait for user response 26

27 Some Useful MATLAB commands who List known variables whos List known variables plus their size help >> help sqrt Help on using sqrt lookfor >> lookfor sqrt Search for keyword sqrt in on MATLABPATH. what >> what ('directory') List MATLAB files in directory clear Clear all variables from work space clear x y Clear variables x and y from work space clc Clear the command window 27

28 Some Useful MATLAB commands dir List all files in current directory ls Same as dir type test Display the content of test.m in command window delete test Delete test.m cd a: Change directory to a: chdir a: Same as cd pwd Show current directory which test Display directory path to closest test.m 28

29 Outline of Lab 2 Review of Lab 1 Matrix in Matlab MATLAB Graphics More Practices 29

30 More Practices Please add variable A and B to Matlab workspace What s the transpose of A? What s the result of (A+B+10)/3? Concatenate A and B horizontally, then vertically. Subtract the 2nd row vector from A. Please clear A and B from Matlab workspace. 30

31 More Practices Make some simple plots: y = sin(x), x [0, 2π] Try to make it smoother by making the step smaller Add x-axis label This is x label and y-axis label This is y label Add a title This is the title Add a legend This is the legend 31

32 Answers of Practices A=[ ; ; ; ]; B=[1+4*j 2+3*j 3+2*j 4+j; 4+j 3+2*j 2+3*j 1+4*j; 2+3*j 3+2*j 4+j 1+4*j; 3+2*j 2+3*j 4+j 1+4*j]; A (A + B + 10)/3 [A, B] [A;B] A(2, :); clear 32

33 Answers of Practices Make some simple plots: x = 0:2*pi; y = sin(x); plot(x,y) This may look a little funny, so try to make it smoother by making the step smaller: x = 0:0.1: 2*pi; y = sin(x); plot(x,y) Add x-axis label This is x label and y-axis label This is y label : xlabel( This is the x label ) ; ylabel( This is the y label ); Add a title This is the title : title( This is the title ); Add a legend This is the legend : legend( This is the legend ); 33

34 What we have learned? 1. Basic matrices manipulation 2. Graphics in Matlab 34

35 Next lab course 1. More about matrices manipulation 2. Matlab file (.m) building 3. More exercises 35